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Search: id:A143068
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| A143068 |
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Expansion of eta(q^2)^5 * eta(q^12) / (eta(q) * eta(q^4) * eta(q^6))^2 in powers of q. |
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2
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| 1, 2, 0, 0, 2, 0, 2, 4, 0, 2, 4, 0, 4, 8, 0, 4, 10, 0, 8, 16, 0, 8, 20, 0, 14, 30, 0, 16, 36, 0, 24, 52, 0, 28, 64, 0, 42, 88, 0, 48, 108, 0, 68, 144, 0, 80, 176, 0, 108, 230, 0, 128, 280, 0, 170, 360, 0, 200, 436, 0, 260, 552, 0, 308, 666, 0, 392, 832, 0, 464, 1000, 0, 584, 1236
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of phi(q) / phi(-q^6) in powers of q where phi() is a Ramanujan theta function.
Euler transform of period 12 sequence [ 2, -3, 2, -1, 2, -1, 2, -1, 2, -3, 2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (96 t)) = (3/2)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A143066.
a(3*n + 2) = 0.
G.f.: ( Sum_{k} x^k^2 ) / ( Sum_{k} (-x^6)^k^2 ).
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EXAMPLE
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1 + 2*q + 2*q^4 + 2*q^6 + 4*q^7 + 2*q^9 + 4*q^10 + 4*q^12 + 8*q^13 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A))^2, n))}
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CROSSREFS
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Sequence in context: A086937 A095759 A046113 this_sequence A028959 A079181 A093693
Adjacent sequences: A143065 A143066 A143067 this_sequence A143069 A143070 A143071
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jul 21 2008
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